Environmental Engineering Reference
In-Depth Information
It should be noted that the temperature in Equation 6.2.31 is in degrees Celsius and
that the emittance values between the two reference points, of 100 C and 400 C, are
nearly linear.
6.2.6.1 Solar irradiation absorption in the glass envelope
As stated in Section 6.2.1, to simplify the model and although physically this is not true,
the solar absorption into the glass envelope wall is treated as a heat flux. In fact, the
solar absorption in the glass envelope wall is a heat generation phenomenon and as
such is a function of the glass wall thickness. However, this assumption introduces
an insignificant error since the glass envelope wall is relatively thin and the solar
absorptance coefficient for glass is very small, 0.02 (Touloukian and DeWitt, 1972).
Additionally, the optical efficiency is used to calculate the solar absorption in the glass
envelope given by:
q go,SolAbs =
q sol η env α env
(6.2.32)
with
η
= γ
ρ cl K θ
(6.2.33)
env
where: q sol =
solar irradiation per receiver length (W/m);
η env =
effective optical effi-
ciency of the glass envelope;
α env =
absorptance of the glass envelope (Pyrex glass);
K
θ =
incident angle modifier, as defined by Equation 6.2.30; and
γ =
intercept factor
[
γ =
e sh e tr e ge e dm e da e ms ].
All parameters in Equation 6.2.33, except the incidence angle modifier (K
), are
taken from the list presented before. Furthermore, the solar irradiation term (q sol )
in Equation 6.2.32 is determined by multiplying the direct normal solar irradiation
(DNI) by the projected normal reflective surface area of the collector, i.e., aperture
area, and dividing by the receiver length. In both equations, all terms are assumed to
be independent of temperature.
θ
6.2.6.2 Solar irradiation absorption in the receiver pipe
As stated before, the solar energy absorbed by the receiver pipe occurs essentially at
the surface; therefore, it is treated as a heat flux (see Section 6.2.1). Therefore, the
equation for the solar absorption in the receiver pipe is given by:
q po,SolAbs =
q sol η abs α abs
(6.2.34)
with:
η abs = η
τ
(6.2.35)
env
env
where:
η abs =
effective optical efficiency at receiver pipe;
α abs =
absorptance of receiver
pipe; and
transmittance of the glass envelope.
In Equation 6.2.34, the effective optical efficiency of the glass envelope,
τ env =
η env is
obtained by Equation 6.2.33 and as before, all terms are assumed to be independent
of temperature.
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